In general, the optimality of a coordination strategy depends on the choice of metric that determines the quality of the FL scheme. A good approach is to consider the aggregation error as the metric and design the coordination strategy, such that the error is minimizedThis is in particular effective, since the MSE of estimated global model directly affects the learning quality of the FL scheme [1]}.. In this case, the optimal coordination strategy is formulated as
\( \left(\mathbf {m}^\star , \mathbf {B}^\star  \right) = \operatornamewithlimits{argmin}_{\mathbf {m}\in \mathbb {C}^N , \left|b_\ell  \right|^2\le P } \epsilon \left( \mathbf {m}, \mathbf {B} \right) .\) 
